Answer:
-24 in^3/sec
Step-by-step explanation:
[tex]V(t) = 2000 - 40t + .2t^2[/tex]
we need to find the rate of change of volume
[tex]\frac{dV}{dt} = \frac{d}{dt} (2000 - 40t + .2t^2)[/tex]
Apply power rule to take dervative
[tex]\frac{dV}{dt} = -40+0.4t[/tex]
we need to find out dv/dt when t=40
Substitute 40 for t
[tex]\frac{dV}{dt} = -40+0.4t[/tex]
[tex]\frac{dV}{dt} = -40+0.4(40)[/tex]
[tex]\frac{dV}{dt} = -40+16[/tex]
[tex]\frac{dV}{dt} =-24[/tex]
so its -24 in^3/sec
